Non-Negative Matrix Division for the Automatic Transcription of Polyphonic Music

In this paper we present a new method in the style of non-negative matrix factorization for automatic transcription of polyphonic music played by a single instrument (e.g., a piano). We suggest using a fixed repository of base vectors corresponding to tone models of single pitches played on a certain instrument. This assumption turns the blind factorization into a kind of non-negative matrix division for which an algorithm is presented. The same algorithm can be applied for learning the model dictionary from sample tones as well. This method is biased towards the instrument used during the training phase. But this is admissible in applications like performance analysis of solo music. The proposed approach is tested on a Mozart sonata where a symbolic representation is available as well as the recording on a computer controlled grand piano.